What is 6ln(x)+4ln(y)-3ln(z) ?

The solution to 6ln(x)+4ln(y)-3ln(z) is ln((x^6y^4)/(z^3))

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simplify 6ln(x)+4ln(y)-3ln(z)

simplify

6 ln (x) + 4 ln (y) - 3 ln (z)

ln (\frac{x ^{6} y ^{4}}{z ^{3}})

Solution steps

6 ln (x) + 4 ln (y) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 ln (x) = ln (x^{6})

= ln (x^{6}) + 4 ln (y) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (y) = ln (y^{4})

= ln (x^{6}) + ln (y^{4}) - 3 ln (z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x^{6}) + ln (y^{4}) = ln (x^{6} y^{4})

= ln (x^{6} y^{4}) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (z) = ln (z^{3})

= ln (x^{6} y^{4}) - ln (z^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{6} y^{4}) - ln (z^{3}) = ln (\frac{x ^{6} y ^{4}}{z ^{3}})

= ln (\frac{x ^{6} y ^{4}}{z ^{3}})

lo g_{10} (\frac{a ^{2} ab}{( ab ) ^{2}})

2 lo g_{10} (x) - 8 lo g_{10} (y)

- lo g_{10} (2 \cdot 1 0^{- 2})

- 1 - lo g_{\frac{1}{3}} (x) - lo g_{\frac{1}{3}} (x + 2)

2 ln (3) + ln (5)

What is 6ln(x)+4ln(y)-3ln(z) ?
The solution to 6ln(x)+4ln(y)-3ln(z) is ln((x^6y^4)/(z^3))